Theory of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math>-shell ionization during nuclear resonance scattering

Abstract

Recently the measured proton-induced C $K$-shell ionization probability was found to vary significantly near the 0.461-MeV $j=\frac{1}{2}+$ elastic resonance in $^{12}\mathrm{C}$. Since the resonance was so wide that time-delay effects on $K$-shell ionization should be very small, it was hypothesized that this effect was due to the exchange of angular momentum between the projectile motion and electron. Assuming a potential description of the nuclear scattering, we make a completely quantum-mechanical calculation of the ionization probability in the distorted-wave Born approximation and show that angular momentum effects do not account for these results. We also show how the amplitude for monopole excitation is augmented by the "shake-off" or "sticking" term found in the semiclassical theory of Ciocchetti and Molinari, and display the formal correspondence between the semiclassical and quantum-mechanical theories. Numerical calculations of the ionization probability show only a slight dip at the minimum in the $p\ensuremath{-}\mathrm{C}$ elastic cross section, opposite in sign and of much smaller magnitude than the reported variation.